Answer/Step-by-step explanation:
1. x*21 = 24*14 (intersecting chords theorem)
21x = 336
x = 336/21
x = 16
2. 27*x = 45² (secant-tangent rule)
27x = 2,025
x = 2,025/27
x = 75
3. (x + 5)*5 = (4 + 6)*6 (Intersecting secants theorem)
5x + 25 = (10)*6
5x + 25 = 60
5x = 60 - 25
5x = 35
x = 35/5
x = 7
4. (4x + 2)*8 = (5x + 1)*7
32x + 16 = 35x + 7
Collect like terms
32x - 35x = -16 + 7
-3x = -9
x = -9/-3
x = 3
ANSWER
The orthocenter is 
<u>EXPLANATION</u>
The orthocenter is the point of intersection of all the altitudes of a triangle.
If it is a right angle triangle then the orthocenter is the point at which the <em>right angle is made.</em>
If it is not a right angle triangle, then you have to find the equations of any two of the altitudes and solve simultaneously.
So you must first check to see if it is a right angle triangle that way you do not have to do bunch work.
The given triangle has vertices 
, , and 
.
Since the denominator is zero, the slope is undefined.
If the slope of a straight line is undefined, then that line is <em>parallel to the y-axis</em>. In other words, it is a <em>vertical line</em>.
if a straight line has a slope of zero, that line is parallel to the <em>x-axis</em> or it is <em>horizontal.</em>
From the slopes we can see that side KL of the triangle is horizontal and side JK is vertical. This two sides will meet at right angles at K.
See graph.
Therefore the coordinates of K, is the orthocenter of the given triangle.
Answer:
1000000 = 1 MLN CODES
Step-by-step explanation:
According the terms of the problems the code has 6 digits or has 6 positions.
At 1st position any of 10 digits (0,1,2,3,4,5,6,7,8 or 9 ) can put
The digits can repeated, so at position 2 any of 10 difits can put.
At position 3 again any of 10 digits can put and similarly for each of next positions can be put any of 10 digits.
So each position of the code has 10 possible variants.
To find the total number of possible codes we have to multiply the number of variants for each position to each other.
N=10*10*10*10*10*10= 10^6=1 000 000
<u>Answer</u>
9+√14
<u>Explanation</u>
To Rationalize the denominator of 5-√7/9-√14.
To rationalize this we multiply both the denominator and denominator by the conjugate of the denominator.
The denominator is 9-√14 and its conjugate is (9+√14).
(5-√7)/(9-√14) = (5-√7)(9+√14)/(9-√14)(9+√14)
= (5-√7)(9+√14)/(9²-14)
= (45 + 5√14 - 9√7 - √98)/(81-14)
= (45 + 5√14 - 9√7 - √98)/67
= (45 + 5√14 - 9√7 - 7√2)67
This is the rationalized expression.
The denominator is (9-√14) and its conjugate is (9+√14).
Answer:
it flip it to the left side and it becomes a p
it flip it to the right side and it becomes a q
Step-by-step explanation:
